Rounding Calculator

How to use the rounding calculator

1. Type the number. Commas are fine. The calculator works on the digits exactly as you type them, so long decimals aren’t disturbed by floating-point error.
2. Choose the place. Pick a place value from millions down to ten-thousandths, or “Multiple of…” to round to an increment such as 0.25, 0.05 or 5.
3. Choose the rule. “Half up” is the rule taught in school. The other four rules are explained below.

The result shows the rounded number, the two neighbors it was chosen from, how much rounding changed the value, and a list with the number rounded to every place under the same rule. It opens on 18.379 rounded to the nearest hundredth: 18.38.

The school rule: round half up

OpenStax’s Prealgebra 2e (section 1.1) describes the method most people learn:

1. Find the place you are rounding to.
2. Look at the digit immediately to its right.
3. If that digit is 5 or more, add 1 to the rounding digit. If it is less than 5, leave the rounding digit alone.
4. Replace every digit to the right with zeros, or drop them after a decimal point.

The textbook’s examples, all reproduced by the calculator:

3,978 shows a carry: adding 1 to the 9 in the hundreds place makes it 10, which carries into the thousands, giving 4,000. And 75 is exactly halfway between 70 and 80; the textbook explains that “so that everyone rounds the same way,” ties go to the higher number, 80.

Round half to even

Rounding every tie up adds a small upward bias when you round many numbers and then add them. Scientific and engineering practice often avoids that bias by sending ties to the even neighbor. NIST’s Guide for the Use of the International System of Units (SP 811, section B.7.1) gives the rule: if the digits being dropped are exactly 5 followed only by zeros, leave the preceding digit unchanged if it is even and raise it by 1 if it is odd.

• 6.974 951 5 to seven digits is 6.974 952 (the 1 is odd, so it goes up).
• 6.974 950 5 to seven digits is 6.974 950 (the 0 is even, so it stays).
• 2.5 rounds to 2 and 3.5 rounds to 4.

Only exact ties are affected. 6.974 951 5 rounded to two digits is 7.0 under both rules, because the dropped digits, 74 951 5, are more than half. This rule is often called banker’s rounding, and it is the default for rounding functions in several programming languages.

Ceiling, floor and truncate

• Ceiling (round up): moves to the next multiple toward positive infinity. You need 2.1 boxes of tile, so you buy 3. Seating 130 guests at tables of 8 needs 17 tables, not 16.25.
• Floor (round down): moves toward negative infinity. With $50 and items at $6 each, you can buy 8; 8.33 is not an option.
• Truncate: drops the extra digits, which moves toward zero. For positive numbers it matches floor; for negatives it matches ceiling, so −2.7 truncates to −2 but floors to −3.

Negative numbers are where rules differ most. Under half up, the calculator rounds −2.5 away from zero to −3, the mirror image of 2.5 → 3. Some spreadsheet and programming functions round −2.5 to −2 instead, so check which rule your software follows.

Rounding to a multiple

Rounding to the nearest ten is rounding to a multiple of 10, and rounding to the nearest hundredth is rounding to a multiple of 0.01. The same idea works for any increment. Choose “Multiple of…” and enter it:

• 0.25: quarter hours on a timesheet or quarter inches on a plan; 7.13 becomes 7.25.
• 0.05: prices or cash amounts to the nearest nickel.
• 5: scores, minutes or temperatures; 12 becomes 10 and 13 becomes 15.

For converting minutes to decimal hours on a timesheet, the time-to-decimal calculator has the common payroll rounding options built in.

Why some calculators round 2.675 to 2.67

Computers store most decimals in binary, which can’t represent 2.675 exactly; the stored value is a hair below it. A program that rounds the stored value to two places gets 2.67, even though the school rule says 2.68. This calculator reads your number as decimal digits and rounds those, so 2.675 becomes 2.68 under half up and 2.68 under half to even (8 is even). Try it with the 2.675 example.

When to round, and estimating

Round once, at the end. Rounding intermediate steps lets small errors pile up. If three people split $100, each share is $33.333…; rounding each share to $33.33 leaves a cent unaccounted for, because 3 × $33.33 = $99.99. The same thing explains why a pie chart of rounded percentages can add up to 99% or 101%: three equal slices of 33.3% total 99.9%.

Rounding is also a fast way to estimate. To check 389 + 512, round both to the nearest hundred: 400 + 500 = 900, close to the exact 901. To check 48 × 21, round to 50 × 20 = 1,000, near the exact 1,008. An estimate won’t give the answer, but it catches a misplaced decimal point or a missing digit.

Rounding to the nearest ten or hundred also makes large numbers easier to read and compare. A city population of 147,032 is easier to quote as about 147,000, and a budget of $29,504 as about $30,000; the textbook uses exactly these kinds of numbers. For reports, say which rule and place you used so others can reproduce the figures.

Be careful with rounding before comparing. 2.449 and 2.451 both round to 2.45, so two values that look equal after rounding may differ, and a value that rounds to a passing grade or a limit may not actually meet it. Compare the unrounded numbers whenever the decision matters. Keep the full value in a spreadsheet and round only what you display.

When a measurement is involved, round to a place that matches how precisely it was measured. A length measured to the nearest tenth of an inch shouldn’t be reported to the thousandth just because a calculator shows more digits.

Sources & assumptions

How this calculator gets its numbers. Full method: our methodology.

• Rounding works on the digits as typed, so 2.675 rounds to 2.68 (no binary floating-point error).
• Half up rounds a tie away from zero (−2.5 → −3); half to even keeps the even neighbor (2.5 → 2, 3.5 → 4).
• Ceiling rounds toward positive infinity, floor toward negative infinity and truncate toward zero.

Sources

1. OpenStax (Rice University), Prealgebra 2e, 1.1 Introduction to Whole Numbers. Rounding whole numbers: 75 to the nearest ten is 80 (ties go up); Example 1.9 (23,658 → 23,700; 3,978 → 4,000) and Example 1.10 (147,032 → 147,000; 29,504 → 30,000).
2. OpenStax (Rice University), Prealgebra 2e, 5.1 Decimals. Rounding decimals: Example 5.9, 18.379 to the nearest hundredth is 18.38; Example 5.10, 18.4 to the nearest tenth and 18 to the nearest whole number.
3. National Institute of Standards and Technology, NIST Guide to the SI (SP 811), B.7.1 Rounding numbers. Rounding rules: when the discarded digits are exactly 5 followed by zeros, the preceding digit is left unchanged if even and increased if odd (6.974 950 5 → 6.974 950; 6.974 951 5 → 6.974 952).

Last reviewed November 2, 2026. Spreadsheet and programming functions differ in how they break ties; check which rule your software uses.